3:15pm

Once more, Mad Ade is waiting for the local Kebab shop to open.
He glances at his clock and notices the time is 3:15pm. Out of sheer boredom Mad Ade works out the angle between the minute and hour hand.

What was the angle between the hour and the minute hands at 3:15pm?

Answer

7.5 degrees

At 3:15, the minute hand will be perfectly horizontal pointing towards 3, whereas the hour hand will be moving towards 4. Also, the hour hand must have covered 1/4 of angle between 3 and 4.

At 30 the hour hand would be on the 3, or at 0 degrees in a standard cartesian coordinate system. The minute hand is at 12, or 90 degrees. The hour hand moves one-twelfth of 360 degrees, or 30 degrees, every hour. Therefore, in fifteen minutes (1/4 hour) it moves 7.5 degrees. In the same time, the minute hand moves to the 3, which is 0 degrees. So the angle between the two hands is 7.5 degrees

The reason this is in Logic (IMHO) is that the actual math involved in this puzzle is trivial. Getting to the math and figuring out the approach, how to solve this, and why it needs solving in the first place (of the first glance the angle ia 0), now that is all logic

I agree with sakirski. The math is trivial once you get past the fact that it will not be zero degress, but the zero degrees part of it is probably the biggest hurdle. AGTMA... Another Great Teaser Mad-Ade.